中間質量ブラックホールからの重力波

真貝寿明  (大阪工業大)

2017/6/23 大阪市立大学セミナー

1

中間質量ブラックホールからの重力波 

GW from merging Intermediate-Mass BHs

http://www.oit.ac.jp/is/~shinkai/

Supermassive BHs 

Intermediate-Mass BHs 

(Stellar-Mass) BHs

10M ⇠ 100M 10 ⁵ M ⇠ 10 ¹⁰ M

10 ² M ⇠ 10 ⁵ M

真貝・神田・戎崎, ApJ, 835 (2017) 276 [arXiv:1610.09505]

contents

1. Gravitational Waves 

       Detectors, GW events  2. Models of SMBH 


       hierarchical growth model,  or others  3. Counting BHs 


        How many BHs in a galaxy? 


        How many galaxies in the Universe? 


4. Event Rates at aLIGO/KAGRA/DECIGO/LISA 


        How many BH mergers in the Universe? 

contents

1. Gravitational Waves 

       Detectors, GW events  2. Models of SMBH 


       hierarchical growth model,  or others  3. Counting BHs 


        How many BHs in a galaxy? 


        How many galaxies in the Universe? 


4. Event Rates at aLIGO/KAGRA/DECIGO/LISA 


        How many BH mergers in the Universe? 

2016年2月，LIGOが重力波を初めて検出した，と発表した

四国新聞だけ 

ちがった．．．残念（笑）

2016年2月，LIGOが重力波を初めて検出した，と発表した

2015年9月14日

2016年2月，LIGOが重力波を初めて検出した，と発表した

毎日新聞 2016/2/13 東京新聞 2016/2/12

「窮理」 2016/８

2017年1月センター試験 国語 小林博司「科学コミュニケーション」

8

2017年1月センター試験 国語 小林博司「科学コミュニケーション」

9

http://www.chugakujuken.net/mailmag̲advice/backnumber/20160229.html

10

http://www.chugakujuken.net/mailmag̲advice/backnumber/20160229.html

https://mediaassets.caltech.edu/gwave

Laser Interferemeter Gravitational-Wave Observatory  （ 1992

年予算承認

)

LIGO （ライゴ：レーザー干渉計重力波天文台）

12

地面振動 

(seismic noise) 熱雑音 

(thermal noise)

Science 256 (1992) 325

量子雑音  (shot noise)

KAGRA （かぐら：大型低温重力波望遠鏡）

http://gwcenter.icrr.u-tokyo.ac.jp/plan/history

Kamioka Gravitational wave detector, (Large-scale Cryogenic Gravitational wave Telescope)

望遠鏡の大きさ：基線長 3km 




望遠鏡を神岡鉱山内に建設 




地面振動が小さい岐阜県飛騨市に ある神岡鉱山 

鏡をマイナス250度（20K）まで 冷却 




熱雑音を小さくするため  鏡の材質としてサファイア




光学特性に優れ、低温に冷却する と熱伝導や機械的損失が少なくな る

15

Science 256 (1992) 325

spectral density [sec]

strain noise signal =  gw  +  noise

16

Science 256 (1992) 325 PRL 116 (2016) 061102

2015/9/16--2016/1/15 Observational run 1 2016/11/30—

Observational run 2

17

  1. Gravitational Wave  >>  Expected Waveform

!25 !20 !15 !10 !5 0 5

!1.0

!0.5 0.0 0.5 1.0

時間

[

ミリ秒

]

合体の時刻 重力波の振幅

連星のインスパイラル運動からの 重力波波形

ブラックホール形成の 重力波波形

× 10 ^{− 22}

NS-NS  NS-BH  BH-BH

h 

time 

Inspiral Merger Ringdown

17

Animation of the inspiral and collision of two black holes consistent with the masses and spins of GW170104. The top part of the movie shows the black hole horizons (surfaces of "no return"). The initial two black holes orbit each other, until they merge and form one larger remnant black hole. The shown black holes are spinning, and angular momentum is exchanged among the two black holes and with the orbit. This results in a quite dramatic change in the orientation of the orbital plane, clearly visible in the movie. Furthermore, the spin-axes of the black holes change, as visible through the colored patch on each black hole horizon, which indicates the north pole.

The lower part of the movie shows the two distinct gravitational waves (called 'polarizations') that the merger is emitting into the direction of the camera. The modulations of the polarizations depend sensitively on the orientation of the orbital plane, and thus encode information about the orientation of the orbital plane and its change during the inspiral. Presently, LIGO can only measure one of the polarizations and therefore obtains only limited information about the orientation of the binary. This disadvantage will be remedied with the advent of additional gravitational wave detectors in Italy, Japan and India.

Finally, the slowed-down replay of the merger at the end of the movie makes it possible to observe the distortion of the newly formed remnant black hole, which decays quickly. Furthermore, the remnant black hole is

"kicked" by the emitted gravitational waves, and moves upward. (Credit: A. Babul/H. Pfeiffer/CITA/SXS.) - See more at: http://ligo.org/detections/GW170104.php#sthash.NZPaW2LT.dpuf

http://ligo.org/detections/GW170104.php

http://www.ligo.org/magazine/LIGO-magazine-issue-8.pdf ¹⁹

!25 !20 !15 !10 !5 0 5

!1.0

!0.5 0.0 0.5 1.0

時間

[

ミリ秒

]

合体の時刻 重力波の振幅

連星のインスパイラル運動からの 重力波波形

ブラックホール形成の 重力波波形

× 10 ^{− 22}

20

  1. Gravitational Wave  >>  Expected Amplitude

KAGRA

. ²¹

  1. Gravitational Wave  >>  Expected Events

1 0 0 1 -‐‑‒ 0 0    

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0.001 0.100 10 1000

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^-23

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f _QNM f _QNM

f _QNM f _QNM

2R _g 5R _g

10R _g 50R _g

10M + 10M 10 ² M + 10 ² M

10 ³ M + 10 ³ M

frequency [Hz]

S tr ai n S en si ti v it y p S n ( f )[ Hz 1 / 2 ]

22

  1. Gravitational Wave  >>  Expected Events

KAGRA

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frequency [Hz]

S tr ai n S en si ti v it y p S n ( f )[ Hz 1 / 2 ]

f _QNM f _QNM

f _QNM f _QNM

2R _g 5R _g

10R _g 50R _g

10M + 10M 10 ² M + 10 ² M

10 ³ M + 10 ³ M

23

  1. Gravitational Wave  >>  Expected Events

KAGRA

.

1 0 0 1 -‐‑‒ 0 0      

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frequency [Hz]

S tr ai n S en si ti v it y p S n ( f )[ Hz 1 / 2 ]

f _QNM f _QNM

f _QNM f _QNM

2R _g 5R _g

10R _g 50R _g

10M + 10M 10 ² M + 10 ² M

10 ³ M + 10 ³ M

10 ^-4 0.01 1 100 10 ^-23

10 ^-21 10 ^-19 10 ^-17

S tr ai n S en si ti v it y p S n ( f )[ Hz 1 / 2 ]

frequency [Hz]

0 0 1 -‐‑‒ 0 0      

10 ³ M + 10 ³ M

10M + 10M

24

  1. Gravitational Wave  >>  Expected Events

.

GW150914

observed by LIGO L1, H1 source type black hole (BH) binary

date 14 Sept 2015

time 09:50:45 UTC

likely distance 0.75 to 1.9 Gly 230 to 570 Mpc redshift 0.054 to 0.136 signal-to-noise ratio 24

false alarm prob. < 1 in 5 million false alarm rate < 1 in 200,000 yr

Source Masses M⊙

total mass 60 to 70

primary BH 32 to 41

secondary BH 25 to 33

remnant BH 58 to 67

mass ratio 0.6 to 1

primary BH spin < 0.7 secondary BH spin < 0.9

remnant BH spin 0.57 to 0.72 signal arrival time

delay

arrived in L1 7 ms before H1 likely sky position Southern Hemisphere

likely orientation face-on/off resolved to ~600 sq. deg.

duration from 30 Hz ~ 200 ms # cycles from 30 Hz ~10

peak GW strain 1 x 10^-21 peak displacement of

interferometers arms ±0.002 fm frequency/wavelength

at peak GW strain 150 Hz, 2000 km peak speed of BHs ~ 0.6 c peak GW luminosity 3.6 x 10⁵⁶ erg s^-1 radiated GW energy 2.5-3.5 M⊙

remnant ringdown freq. ~ 250 Hz ^. remnant damping time ~ 4 ms ^.

remnant size, area 180 km, 3.5 x 10⁵ km² consistent with

general relativity?

passes all tests performed graviton mass bound < 1.2 x 10^-22 eV

coalescence rate of

binary black holes 2 to 400 Gpc^-3 yr^-1 online trigger latency ~ 3 min # offline analysis pipelines 5

CPU hours consumed ~ 50 million (=20,000 PCs run for 100 days) papers on Feb 11, 2016 13

# researchers ~1000, 80 institutions in 15 countries B A C K G R O U N D I M A G E S : T I M E - F R E Q U E N C Y T R A C E ( T O P ) A N D T I M E - S E R I E S

( B O T T O M ) I N T H E T W O L I G O D E T E C T O R S ; S I M U L A T I O N O F B L A C K H O L E H O R I Z O N S ( M I D D L E - T O P ) , B E S T F I T W A V E F O R M ( M I D D L E - B O T T O M )

G W 1 5 0 9 1 4 : F A C T S H E E T

first direct detection of gravitational waves (GW) and first direct observation of a black hole binary

Detector noise introduces errors in measurement. Parameter ranges correspond to 90% credible bounds.

Acronyms: L1=LIGO Livingston, H1=LIGO Hanford; Gly=giga lightyear=9.46 x 10¹² km; Mpc=mega parsec=3.2 million lightyear, Gpc=10³ Mpc, fm=femtometer=10^-15 m, M⊙=1 solar mass=2 x 10³⁰ kg

13億光年先 

（400 170 Mpc） 

（z=0.054̶0.136） 

36Msun + 29 Msun 

のBHが合体して 62 Msun 

（3 Msun分の質量が消失） 

重力波が検出された！ 

重力波が検出できた！ 

BHが存在した！ 

BH連星が存在した！ 

相対論が第0近似で正しい！

observed by LIGO L1, H1 source type black hole (BH) binary

date 14 Sept 2015

time 09:50:45 UTC

likely distance 0.75 to 1.9 Gly 230 to 570 Mpc redshift 0.054 to 0.136 signal-to-noise ratio 24

false alarm prob. < 1 in 5 million false alarm rate < 1 in 200,000 yr

Source Masses M⊙

total mass 60 to 70

primary BH 32 to 41

secondary BH 25 to 33

remnant BH 58 to 67

mass ratio 0.6 to 1

primary BH spin < 0.7 secondary BH spin < 0.9

remnant BH spin 0.57 to 0.72 signal arrival time

delay

arrived in L1 7 ms before H1 likely sky position Southern Hemisphere

likely orientation face-on/off resolved to ~600 sq. deg.

duration from 30 Hz ~ 200 ms # cycles from 30 Hz ~10

peak GW strain 1 x 10^-21 peak displacement of

interferometers arms ±0.002 fm frequency/wavelength

at peak GW strain 150 Hz, 2000 km peak speed of BHs ~ 0.6 c peak GW luminosity 3.6 x 10⁵⁶ erg s^-1 radiated GW energy 2.5-3.5 M⊙

remnant ringdown freq. ~ 250 Hz ^. remnant damping time ~ 4 ms ^.

remnant size, area 180 km, 3.5 x 10⁵ km² consistent with

general relativity?

passes all tests performed graviton mass bound < 1.2 x 10^-22 eV

coalescence rate of

binary black holes 2 to 400 Gpc^-3 yr^-1 online trigger latency ~ 3 min # offline analysis pipelines 5

CPU hours consumed ~ 50 million (=20,000 PCs run for 100 days) papers on Feb 11, 2016 13

# researchers ~1000, 80 institutions in 15 countries B A C K G R O U N D I M A G E S : T I M E - F R E Q U E N C Y T R A C E ( T O P ) A N D T I M E - S E R I E S

( B O T T O M ) I N T H E T W O L I G O D E T E C T O R S ; S I M U L A T I O N O F B L A C K H O L E H O R I Z O N S ( M I D D L E - T O P ) , B E S T F I T W A V E F O R M ( M I D D L E - B O T T O M )

G W 1 5 0 9 1 4 : F A C T S H E E T

first direct detection of gravitational waves (GW) and first direct observation of a black hole binary

Detector noise introduces errors in measurement. Parameter ranges correspond to 90% credible bounds.

Acronyms: L1=LIGO Livingston, H1=LIGO Hanford; Gly=giga lightyear=9.46 x 10¹² km; Mpc=mega parsec=3.2 million lightyear, Gpc=10³ Mpc, fm=femtometer=10^-15 m, M⊙=1 solar mass=2 x 10³⁰ kg

Draft:

DCC

P151226-v10

- do

not circulate

duration from 35 Hz ~1 s # cycles from 35 Hz ~55

signal arrival time

delay arrived in H1 1 ms after L1

peak GW strain ~ 3.4 x 10^-22 peak displacement of

interferometers arms ~ ±0.7 am frequency/wavelength

at peak GW strain 420 Hz, 710 km peak speed of BHs ~ 0.6 c

peak GW luminosity 2 to 4 x 10⁵⁶ erg s^-1 radiated GW energy 0.8-1.1 M⊙

remnant ringdown freq. ~ 750 Hz . remnant damping time ~ 1.3 ms .

remnant size, area 60 km, 3.5 x 10⁴ km² online trigger latency ~ 67 s

# offline analysis pipelines 2

Draft:

DCC

P151226-v10

- do

not circulate

Draft:

DCC

P151226-v10

- do

not circulate

observed by LIGO L1, H1 source type black hole (BH) binary

date 26 Dec 2015

time 03:38:53 UTC

distance 250 to 620 Mpc

redshift 0.05 to 0.13

signal-to-noise ratio 13

false alarm prob. ~ 1 in 10 million Source Masses M⊙

total mass 20 to 28

primary BH 11 to 23

secondary BH 5 to 10

remnant BH 19 to 27

mass ratio > 0.28

spin of one of the

black holes > 0.2

remnant BH spin 0.7 to 0.8 resolved to ~850 sq. deg.

Parameter ranges correspond to 90% credible bounds. Acronyms: L1/H1=LIGO Livingston/Hanford; Mpc=mega parsec=3.2 million lightyear, am=attometer=10^-18 m,

M⊙=1 solar mass=2 x 10³⁰ kg

B A C K G R O U N D I M A G E S : T I M E - F R E Q U E N C Y T R A C E ( T O P ) A N D S I G N A L - T O - N O I S E R A T I O T I M E - S E R I E S ( B O T T O M ) I N T H E T W O

L I G O D E T E C T O R S ; E X A M P L E W A V E F O R M ( M I D D L E )

G W 1 5 1 2 2 6 : F A C T S H E E T

GW151226

15億光年先 

（440 190 Mpc） 

（z=0.05̶0.13） 

14Msun + 7.5 Msun 

のBHが合体して 21 Msun 

（1 Msun分の質量が消失） 

GW170104

http://ligo.org/detections/GW170104.php

Comparison of gravitational-wave signal templates from recent LIGO observations. This figure shows reconstructions of the three confident and one candidate (LVT151012) gravitational wave signals detected by LIGO to date, including the most recent detection GW170104. Each row shows the signal arriving at the Hanford detector as a function of time. The thickness of the curves indicates the 90%

confidence interval on the model parameters. Only the portion of each signal that LIGO was sensitive to is shown here (the final seconds leading up to the black hole merger). [Credit: LIGO/B. Farr (U.

Chicago)] - See more at: http://ligo.org/detections/GW170104.php#sthash.QTJIckcl.dpuf

http://ligo.org/detections/GW170104.php

32

  1. Gravitational Wave  >>  Expected Events

LIGO/KAGRA

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Sky Map of LIGO's Black-Hole Mergers. This three- dimensional projection of the Milky Way galaxy onto a transparent globe shows the probable locations of the three confirmed LIGO black-hole merger events—

GW150914 (blue), GW151226 (orange), and the most recent detection GW170104 (magenta)—and a fourth possible detection, at lower significance (LVT151012, green). The outer contour for each represents the 90 percent confidence region; the innermost contour signifies the 10 percent confidence region. [Image credit:

LIGO/Caltech/MIT/Leo Singer (Milky Way image: Axel Mellinger)] - See more at: http://ligo.org/detections/

GW170104.php#sthash.pwWdVLL4.dpuf

Forecasting LIGO Detections in the Three-Detector Era. This map illustrates how the addition of the Virgo detector, scheduled to come online this summer, could improve the localization of sources of gravitational waves. The map shows the estimated locations of the four black-hole merger events detected by LIGO to date (including one event seen at lower significance), after including hypothetical Virgo data. Outer contours represent the 90 percent confidence region; innermost contours signify the 10 percent confidence region. [Image credit: LIGO/Caltech/

MIT/Leo Singer (Milky Way image: Axel Mellinger)] - See more at: http://ligo.org/

detections/GW170104.php#sthash.NZPaW2LT.dpuf

http://ligo.org/detections/GW170104.php

M1+M2=Mf,   Mdiff/Mtotal 


a̲final

Mpc 

z SNR deg^2

GW150914

PRL116,  061102 
 (2016/2/11)

36.2+29.1=62.3+3.0 
 4.59% 


0.68

410Mpc 

0.09 24 600

LVT151012 (2016/2/11)

23+13=35+1.5 
 2.78% 


0.66 GW151226

PRL116,  241103 
 (2016/6/15)

14.2+7.5=20.8+0.9 
 4.15% 


0.74

440Mpc 

0.09 13 850

GW170104

PRL118,  221101 
 (2017/6/1)

31.2+19.4=48.7+1.9 
 3.75% 


0.64

880Mpc 

0.18 13 1300

https://losc.ligo.org/events/GW150914/

https://losc.ligo.org/events/GW151226/

https://losc.ligo.org/events/LVT151012/

https://losc.ligo.org/events/GW170104/

arXiv:1606.01262

http://ligo.org/detections/GW170104.php

why not more?

38

  1. Gravitational Wave  >>  Expected Waveform

!25 !20 !15 !10 !5 0 5

!1.0

!0.5 0.0 0.5 1.0

時間

[

ミリ秒

]

合体の時刻 重力波の振幅

連星のインスパイラル運動からの 重力波波形

ブラックホール形成の 重力波波形

× 10 ^{− 22}

NS-NS  NS-BH  BH-BH

Inspiral Merger Ringdown

h 

time 

38

39 S tr ai n n oi se am p li tu d e[ 1 / p Hz ]

frequency[Hz]

1 10 100 1000 10⁴

10^-25 10^-22 10^-19 10^-16

Kagra

TOBA

aLIGO aVIRGO

ET

10 100 1000 10

⁴

10 100 1000 10

⁴

a = 0.0

a = 0.5 a = 0.9

M _BH /M

fr eq u en cy [Hz ]

地上での重力波干渉計感度

BH quasi-normal freq. 

(ringdown freq.)

BH < 2000Msun can be a target 

IMBH ringdown freq.  is detectable at LIGO/KAGRA

10Hz 1000Hz

1000M 100M

10

100 _f

qnm = c ³

2⇡ GM _T 1 0.63(1 a) ^0.3

contents

1. Gravitational Waves 

       Detectors, GW events  2. Models of SMBH 


       hierarchical growth model,  or others  3. Counting BHs 


        How many BHs in a galaxy? 


        How many galaxies in the Universe? 


4. Event Rates at aLIGO/KAGRA/DECIGO/LISA 


        How many BH mergers in the Universe? 

Rees, M.J. 1978. Observatory 98: 210 41

  2. Models of SMBH

Volonteri, Science 337 (2012) 544

42

  2. Models of SMBH

Greene, Nature Comm 3 (2012)  [arXiv:1211.7082]

43

  2. Models of SMBH

Rees, M.J. 1978. Observatory 98: 210 44

Gas Cloud

BHs

IMBHs

SMBHs

Halo

Galaxy Globular 

Cluster Massive 

Stars

 Ebisuzaki +, ApJ, 562, L19 (2001)

  2. Models of SMBH

45

Yagi, CQG 29 075005 (2012)   [arXiv:1202.3512]

HLX-1 has 20,000M BH!

http://hubblesite.org/newscenter/archive/releases/2012/2012/11/full/

Starburst galaxy M82 has 1000M BH

BHs

IMBHs

SMBHs

Matsushita+, ApJ, 545, L107 (2000)    Matsumoto+, ApJ, 547, L25 (2001)  

 Ebisuzaki +, ApJ, 562, L19 (2001)

0.15pc from SgrA* 

1-2 x 10 ⁴  Msun 1602.05325

46

PortegiesZwart+, ApJ 641(2006)319

47

48

BHs

IMBHs

SMBHs

'Missing link' founded 

      Ebisuzaki +, ApJ, 562, L19 (2001)   
 (1)formation of IMBHs by runaway mergers of 

massive stars in dense star clusters,  

(2) accumulations of IMBHs at the center region of  a galaxy due to sinkages of clusters by dynamical  friction 

(3) mergings of IMBHs by multi-body interactions  and gravitational radiation. 

Marchant & Shapiro 1980; Portegies Zwart et al. 1999;  

Portegies Zwart & McMillan 2002;  

Portegies Zwart et al. 2004;  

Holger & Makino 2003

Matsubayashi et al. 2007 

Iwasawa et. al. 2010  

雰囲気（巡り逢い）＋仲良し成長 モデル

Matsubayashi, HS, Ebisuzaki, ApJ 614 (2004) 864

IMBH-IMBH mergers produce low freq. GW 

51

52

Matsubayashi, HS, Ebisuzaki, ApJ 614 (2004) 864 ₅₃

How many BH mergers  in the Universe? 

How many BH mergers  we observe in a year?

How many BHs in a galaxy? 

How many galaxies in the Universe?

Detectable Distance ?     KAGRA/aLIGO/aVIRGO Cosmological model? 

BH spin?  Signal-to-Noise?

54

contents

1. Gravitational Waves 

       Detectors, GW events  2. Models of SMBH 


       hierarchical growth model,  or others  3. Counting BHs 


        How many BHs in a galaxy? 


        How many galaxies in the Universe? 


4. Event Rates at aLIGO/KAGRA/DECIGO/LISA 


        How many BH mergers in the Universe? 

56

Mass Function of Giant Molecular Clouds

1 100 10

⁴

10

⁶

10

^-4

1 10

⁴

10

⁸

10

¹²

M 10 ¹² M

10 ⁹ M

galaxy mass

GMC mass

A&A 580, A49 (2015) [arXiv:1505.04696] 

How many BHs in a Galaxy?

57

10 100 1000 10

⁴

10

^-7

0.001 10.000 10

⁵

1309.1223v3

10 ¹² M

10 ⁹ M

Galaxy Mass n(M)

BH mass

Molecular Clouds  

       Maximum Core      

Building Block BH 

How many BHs in a Galaxy?

58

Count BHs to form a SMBH

10 1000 10⁵ 10⁷ 10⁹ 10¹¹

10^-7 10^-4 0.1 100 10⁵

10 100 1000 10

⁴

10

^-7

0.001 10.000 10

⁵

10 ¹² M

10 ⁹ M

Galaxy Mass n(M)

BH mass

Building Block BH 

BH mass n(M)

How many BHs in a Galaxy?

59

Count BHs to form a SMBH

10 1000 10⁵ 10⁷ 10⁹ 10¹¹

10^-7 10^-4 0.1 100 10⁵

dynamical friction

BH mass n(M)

How many BHs in a Galaxy?

60

(sub-)Galaxy 

from Halo model  

Star Formation Rate  

peak z=3.16

Count BHs to form a SMBH

How many Galaxies in the Universe?

61

10¹¹ 10¹² 10¹³ 10¹⁴ 10¹⁵

10^-23 10^-21 10^-19 10^-17 10^-15 10^-13

z = 0 z = 5

10¹² 10¹³ 10¹⁴ 10¹⁵

5 10 50 100 500 1000

(1) Halo number density

(2) N of seeds of Galaxy (subHalo)

(3) N of Galaxy 

within z=1 within z=5

M ¹

1×10¹¹ 5×10¹¹ 1×10¹² 5×10¹²

0.01 1 100

M ^1.95

How many Galaxies in the Universe?

z<3 

10 ¹²    

62 https://www.ras.org.uk/news-and-press/2910-a-universe-of-two-trillion-galaxies

http://iopscience.iop.org/article/10.3847/0004-637X/830/2/83

x10 more than before 

# of galaxy (z<8) : 2x10 ¹² 

# of galaxy 10 ⁶ >Msun  


   reduces in evolution

63

(sub-)Galaxy 

from Halo model  

Star Formation Rate  

peak z=3.16

Count BHs to form a SMBH

How many Galaxies in the Universe?

McConnell-Ma 

ApJ 764(2013)184

64

contents

1. Gravitational Waves 

       Detectors, GW events  2. Models of SMBH 


       hierarchical growth model,  or others  3. Counting BHs 


        How many BHs in a galaxy? 


        How many galaxies in the Universe? 


4. Event Rates at aLIGO/KAGRA/DECIGO/LISA 


        How many BH mergers in the Universe? 

66

図F

BH mass

z z

BH mass

in Standard Cosmology

How many BH mergers in the Universe?

Event Rate R[/yr] = N _merger (z) V (D/2.26)

Standard Cosmology

averaging distances  

for all directions

Signal-to-Noise Ratio (SNR)

Strainnoiseamplitude[1/√ Hz]

frequency[Hz]

Kagra

TOBA

aLIGO aVIRGO

ET

67

68

Detectable Distances at bKAGRA

Hierarchical Growth   

⇢ ² = 8 5

✏ _r (a) f _R ²

(1 + z)M S _h (f _R /(1 + z))

✓ (1 + z)M d _L (z )

◆ 2 ✓ 4µ M

◆ 2

SNR

Energy emission=4% of total M，1% at ringdown Flanagan&Hughes, PRD57(1998)4535

Standard Cosmology

a = 0.9

KAGRA KAGRA

Slide copy from Hiroyuki Nakano

69

GW150914 4.7% of mass 

emitted  in total 2.8% of mass 

emitted by ISCO

1% of mass 

emitted  

in ringdown?

70

図F

BH mass

z z

BH mass

in Standard Cosmology

How many BH mergers in the Universe?

Event Rate R[/yr] = N _merger (z) V (D/2.26)

Standard Cosmology

averaging distances  

for all directions

Event Rates at bKAGRA

BH spin=0.9,0.5,0.0

peak at 60M

range 40M-150M

7 events/yr

210 events/yr

71

Event Rates at bKAGRA/aLIGO

7 events/yr

peak at 60M

BH mass (final BH) [M ] BH mass (final BH) [M ]

E ve n t R at e [1 / yr]

(a1) SNR=10, KAGRA (a2) SNR=10, KAGRA

10 50 100 500 1000 5000 10⁴

0.5 1 5 10 50 100

N merger

10 50 100 500 1000 5000 10⁴

10⁷ 10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹²

range 40M-150M

210 events/yr

LIGO group [1602.03842]

Inoue+ MNRAS461(16)4329

6-400 /Gpc^3/yr

Kinugawa+ MNRAS456(15)1093

70-140 /yr

72

Event Rates at bKAGRA/aLIGO

7 events/yr

peak at 60M

BH mass (final BH) [M ] BH mass (final BH) [M ]

E ve n t R at e [1 / yr]

(a1) SNR=10, KAGRA (a2) SNR=10, KAGRA

10 50 100 500 1000 5000 10⁴

0.5 1 5 10 50 100

N merger

10 50 100 500 1000 5000 10⁴

10⁷ 10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹²

range 40M-150M

210 events/yr

LIGO group PRX6(2016)041015 

Inoue+ MNRAS461(16)4329

6-400 /Gpc^3/yr

Kinugawa+ MNRAS456(15)1093

70-140 /yr

73

10 ^-4 0.01 1 100 10 ^-23

10 ^-21 10 ^-19 10 ^-17

S tr ai n S en si ti v it y p S n ( f )[ Hz 1 / 2 ]

frequency [Hz]

0 1 0 0 10 0 0

10 ³ M + 10

3 M

10 ² M + 10

2 M 10 ⁴ M + 10

4 M

74

http://rhcole.com/apps/GWplotter/

これは遊べる GWplotter

75

10⁵ 10⁶ 10⁷ 10⁸ 10⁷

10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹²

観測できるBH数分布 1年間で観測できるBH数分布 

(S/N=10)

spin 0.9

spin 0

BH質量[Msun]

BH質量[Msun]

年55個

10⁴ 10⁵ 10⁶ 10⁷ 10⁸

0.10 1 10 100

10⁴ 10⁵ 10⁶ 10⁷ 10⁸ 10⁹

10 100 1000 10⁴

観測できるBH合体距離  (S/N=10)

BH質量[Msun]

[Mpc]

10^-4 0.01 1 100

10^-23 10^-21 10^-19 10^-17

eLISA N2A5

76

Event Rates at eLISA

観測できるBH数分布 1年間で観測できるBH数分布 

(S/N=10)

spin 0.9

spin 0

BH質量[Msun]

BH質量[Msun]

観測できるBH合体距離  (S/N=10)

BH質量[Msun]

[Mpc]

10^-4 0.01 1 100

10^-23 10^-21 10^-19 10^-17

PreDECIGO

100 1000 10⁴ 10⁵ 10⁶ 10⁷

0.10 1 10 100 1000

100 1000 10⁴ 10⁵ 10⁶ 10⁷

10⁷ 10⁹ 10¹¹ 10¹³

1 10 100 1000 10⁴ 10⁵ 10⁶

1 10 100 1000 10⁴ 10⁵

77

Event Rates at PreDECIGO

100 1000 10⁴ 10⁵ 10⁶ 10⁷ 10⁷

10⁹ 10¹¹ 10¹³

観測できるBH数分布 1年間で観測できるBH数分布 

(S/N=30)

spin 0.9

spin 0

BH質量[Msun]

BH質量[Msun]

観測できるBH合体距離  (S/N=30)

BH質量[Msun]

[Mpc]

10^-4 0.01 1 100

10^-23 10^-21 10^-19 10^-17

PreDECIGO

1 10 100 1000 10⁴ 10⁵ 10⁶

10 100 1000 10⁴

100 1000 10⁴ 10⁵ 10⁶ 10⁷

0.10 1 10 100

1000 年4850個

78

Event Rates at PreDECIGO

BH spin=0.9,0.5,0.0

まとめ

重力波検出のデータを蓄積することによって，銀河分布やSMBH形成シナリオを特定 したり，宇宙膨張モデルの検証や，重力理論の検証が可能になる．

SMBHの形成シナリオとして， IMBHsの合体を経由するボトムアップシナリオ を仮定して，重力波検出頻度を計算した． 

モデルの仮定： 

 分子雲のコアが10Msun以上になったら，BHになると仮定した． 

 BHは等質量同士のものが次々に合体して成長していくものと仮定した． 

 BHが形成された後，ガス降着で太ることは考慮していない． 

 銀河数分布は，サブハローモデルと，星形成率を乗じたものから計算した． 

 SMBHは，宇宙初期のガスのdirect collapseによって生じたという説もあるが， 

 そのような形成仮定があれば，このモデルで得た検出頻度は減る． 


 リングダウン部分の重力波を直接検出できる，と仮定した． 

. 79